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Chapter 24The Wave Nature
of Light
AP Physics BMrs. Wallace
24-01 Conditions for Interference
24-02 Young’s Double-Slit Experiment
24-03 Change of Phase Due to Reflection
24-04 Interference in Thin Films
24-06 Diffraction
24-07 Single-Slit Diffraction
24-08 The Diffraction Grating
Wave Optics
Sections
Wave Optics 24 (02 of 41)
Conditions for Interference
For observable interference effects, sources must be
1. Coherent
2. Monochromatic
Waves must maintain a constant phase
relationship
Waves must have the same wavelength
Wave Optics 24 (03 of 41)
Chapter 24: Wave Optics
Two light sources are said to be coherent if they
(A) are of the same frequency.
(B) are of the same frequency, and maintain a constant phase difference.
(C) are of the same amplitude, and maintain a constant phase difference.
(D) are of the same frequency and amplitude.
Wave Optics 24 (04 of 41)
If light is a wave, interference effects will be seen, where one part of wavefront can interact with another part.
One way to study this is to do a double-slit experiment:
Young’s Double-Slit Experiment
Wave Optics 24 (05 of 41)
Young’s Double-Slit Experiment
Wave Optics 24 (06 of 41)
The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).
Young’s Double-Slit Experiment
Wave Optics 24 (07 of 41)
Chapter 24: Wave Optics
What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits?
(A) refraction
(B) polarization
(C) dispersion
(D) interference
Wave Optics 24 (08 of 41)
We can use geometry to find the conditions for constructive and destructive interference:
.... 2, 1, ,0m ,λmθsind
Bright(constructive interference)
.... 2, 1, ,0m ,λ mθsind21
Dark(destructive interference)
Young’s Double-Slit Experiment
Wave Optics 24 (09 of 41)
S1
S2
PS2 - PS1= d sin()
Constructive Interference
. . . 2, 1, ,0m λm)θsin(d
Destructive Interference
. . . 2, 1, ,0m λ 21
m)θsin(d
screen
P
d
Young’s Double-Slit Experiment
Wave Optics 24 (10 of 41)
S1
S2
screen
Bright
d
y
L
Ly
)θtan()θsin(
dλmL
y )bright(
Constructive Interference
dλL
yΔ
2, 1, ,0m λmθsind
Young’s Double-Slit Experiment
Wave Optics 24 (11 of 41)
S1
S2
d
screen
Dark
Ly
)θtan()θsin(
dλL
yΔ
L
y
d
λL21
my dark
Destructive Interference
. . . 2, 1, ,0m
21
m)θsin(d
Young’s Double-Slit Experiment
Wave Optics 24 (12 of 41)
Chapter 24: Wave Optics
In a Young's double slit experiment, if the separation between the slits decreases, what happens to the distance between the interference fringes?
(A) It decreases.
(B) It increases.
(C) It remains the same.
(D) There is not enough information to determine.
dλL
yΔ
Wave Optics 24 (13 of 41)
Chapter 24: Wave Optics
At the first minima on either side of the central bright spot in a double-slit experiment, light from each opening arrives
(A) in phase.
(B) 90° out of phase.
(C) 180° out of phase.
(D) none of the given answers
Wave Optics 24 (14 of 41)
Chapter 24: Wave Optics
At the second maxima on either side of the central bright spot in a double-slit experiment, light from
(A) each opening travels the same distance.
(B) one opening travels twice as far as light from the other opening.
(C) one opening travels one wavelength of light farther than light from the other opening.
(D) one opening travels two wavelengths of light farther than light from the other opening.
Wave Optics 24 (15 of 41)
Chapter 24: Wave Optics
What principle is responsible for light spreading as it passes through a narrow slit?
(A) refraction
(B) polarization
(C) diffraction
(D) interference
Wave Optics 24 (28 of 41)
Diffraction
Wave Optics 24 (27 of 41)
The resulting pattern of light and dark stripes is called a diffraction pattern.
This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would.
The minima of the single-slit diffraction pattern occur when
.... ,3 ,2 ,1m
λmθsin D
Single-Slit Diffraction
Wave Optics 24 (29 of 41)
d
L dλ2
2
dλ
1
dλ
1
dλ2
2
θsin y
θsin y
0θsin 0
θsin y
θsin y
Single-Slit Diffraction
Wave Optics 24 (30 of 41)
Chapter 24: Wave Optics
A person gazes at a very distant light source. If she now holds up two fingers, with a very small gap between them, and looks at the light source, she will see
(A) the same thing as without the fingers, but dimmer.
(B) a series of bright spots.
(C) a sequence of closely spaced bright lines.
(D) a hazy band of light varying from red at one side to blue or violet at the other.
Wave Optics 24 (31 of 41)
dλ
θsin
Ly
θtan
θtanθsin
Ly
dλ
dλL
y
m 10x 3.00
m 10x5.6m 5.24
7
m 0.0054y
yd
A single slit of width 0.30 mm is illuminated with 650 nm light. Aninterference pattern is formed on a screen 2.5 m away. Find the distancefrom the first dark band to the centralbright band.
Single-Slit Diffraction
Wave Optics 24 (32 of 41)
2 m λmθsin D
A single slit of width 0.14 mm is illuminated by monochromatic light and interference bands are observed on a screen 2.0 m away.If the second dark band is 16 mm from the central bright band,what is the wavelength of the light?
D
L
y
Dλ2
θsin
θsinLy
θtan Dλ2
Ly
L2yD
λ m 0.22
m 00014.0m 016.0
nm 560 m 10 x 6.5λ 7
Single-Slit Diffraction
Wave Optics 24 (33 of 41)
A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light.
The more lines or slits there are, the narrower the peaks.
Two slits
Six slits
The Diffraction Grating
Wave Optics 24 (34 of 41)
Chapter 24: Wave Optics
Consider two diffraction gratings with the same slit separation, one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light, make a statement concerning the separation between the orders.
(A) The grating with 3 slits produces the greater separation between orders.
(B) The grating with 4 slits produces the greater separation between orders.
(C) Both gratings produce the same separation between orders.
(D) Both gratings produce the same separation between orders, but the orders are better defined with the 4-slit grating.
Wave Optics 24 (35 of 41)
The maxima of the diffraction pattern are defined by
...... 3, 2, 1, ,0m ,λmθsind
The Diffraction Grating
Wave Optics 24 (36 of 41)
A 3500-line/cm grating produces a third-order fringe at a 28.0o angle. What is the wavelength of light being used?
λmθsind
mθsind
λ
3
0.28sin
mlines
000,350
1
λ
o
m 10 x 47.4 7
mn 447
The Diffraction Grating (Problem)
Wave Optics 24 (37 of 41)
A diffraction grating has 6.0 x 105 lines/m. Find the angular spread in second-order spectrum between red light of wavelength
7.0 x 107 m and blue light of wavelength 4.5 x 107 m.RB
R
B
m = 2
line/m 10 x 0.6
1m 10 x 0.72
sinθ
5
71
R o1.57
line/m 10 x 0.6
1m 10 x 5.42
sinθ
5
71
Bo7.32
ooo 4.24 7.321.57θΔ
λmθsind
The Diffraction Grating (Problem)
Wave Optics 24 (39 of 41)
A spectrometer makes accurate measurements of wavelengths using a diffraction grating or prism.
The Spectrometer and Spectroscopy
The Diffraction Grating
Wave Optics 24 (39 of 41)
The wavelength can be determined to high accuracy by measuring the angle at which the light is diffracted.
Atoms and molecules can be identified when they are in a thin gas through their characteristic emission lines.
θsinmd
λ
The Spectrometer and Spectroscopy
The Diffraction Grating
Wave Optics 24 (40 of 41)
Change of Phase Due to Reflection
A reflected light wave undergoes a phase change of 180o.
Wave Optics 24 (16 of 41)
Change of Phase Due to Reflection
A reflected light wave undergoes no phase change.
Wave Optics 24 (17 of 41)
Chapter 24: Wave Optics
When a beam of light, which is traveling in glass, strikes an air boundary, there is
(A) a 90° phase change in the reflected beam.
(B) a 180° phase change in the reflected beam.
(C) a 45° phase change in the reflected beam.
(D) no phase change in the reflected beam.
Wave Optics 24 (18 of 41)
glass
air
air
Another way path lengths can differ, and waves interfere, is if they travel through different media.
If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference.
This can be seen in soap bubbles and oil slicks, for example.
changephase
λ 21
changephase
oN
Interference in Thin Films
Wave Optics 24 (19 of 41)
t
(maxima)Bright λt
(minima) Dark λt
If
41
21
Interference in Thin Films
Wave Optics 24 (20 of 41)
t
a
bThe phase displacement of (b) relative to (a) is
reflection to Due λ21
difference path to Due tn2
m ... , , , is tn2 When21
25
23
21
21
m ... ,3 ,2 , is tn2 When21
There is darkness
There is brightness
n
Interference in Thin Films
Wave Optics 24 (21 of 41)
n = 1.0
a
b
air
kerosene
water
n’ = 1.2
n’’ = 1.3
t
A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are looking straight down from an airplane onto a region of the slick where its thickness is t = 460 nm.Which wavelength of visible light is reflected the greatest?
λmtn'2
mtn'2
λ
m
2.1 nm 6042λ
nm 1104λ 1m
nm 552λ 2m
nm 368λ 3m
Interference in Thin Films (Problem)
Wave Optics 24 (22 of 41)
A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are a scuba-diver directly under the slick where its thickness is t = 460 nm.Which wavelength of visible light is the transmitted intensitythe greatest?
λmtn'2λ21
21m
tn'2λ
21m
2.1nm 6042λ
nm 2208λ 1m
nm 736λ 2m
nm 441λ 3m
n = 1.0
a b
air
kerosene
water
n’ = 1.2
n’’ = 1.3
t
nm 315λ 4m
Interference in Thin Films
Wave Optics 24 (23 of 41)
One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass.
Interference in Thin Films
Wave Optics 24 (24 of 41)
BRIGHT
BRIGHT
DARK
0 t 2λ
t λ t
21
mt2 Dark21
m = 0 m = 1 m = 2
DARK
DARK
Interference in Thin Films
Wave Optics 24 (25 of 41)
Problem Solving: Interference
Interference occurs when two or more waves arrive simultaneously at the same point in space.
Constructive interference occurs when the waves are in phase.
Destructive interference occurs when the waves are out of phase.
An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.
Interference in Thin Films
Wave Optics 24 (26 of 41)